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If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c.
I know how to set this up and solve it, but for some reason I can't get the right answer.
 one year ago
 one year ago
If the direction angle of vector a is 100 degrees, with a magnitude of 8, and the direction angle of vector c is 60 degrees, with a mangitude of 13, find the magnitude of resultant a + c. I know how to set this up and solve it, but for some reason I can't get the right answer.
 one year ago
 one year ago

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thechocoluver445Best ResponseYou've already chosen the best response.1
Here's what I did: dw:1358034696496:dw \[x = \sqrt{8^2 + 13^2  2(8)(13)(\cos 140°)}\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.0
Hmmm this is how I would do it :O So if we write our vectors in component form, we have,\[\large \vec{a}=8\cos100 \hat i+8\sin100 \hat j\]\[\large \vec c=13\cos60 \hat i+13\sin60 \hat j\]\[\large \vec a +\vec c=\color{#3366CF}{(8\cos100+13\cos60)\color{black}{\hat i}+(8\sin100+13\sin60)\color{black}{\hat j}}\] Hmm since 100 degrees isn't a nice special angle, we're going to get ugly decimal values it seems... So punch that into the calculator, then to get the MAGNITUDE of that vector we'll do uhhhh the thing, yah... I'm a little confused where your formula for x is coming from. It looks similar to the law of cosines. Maybe I just haven't done these types of problems in too long c: heh
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
Yeah I used law of cosines. If I add up all of the things in your method, I don't get the correct answer.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.0
ah ok c: lemme take another shot at it. sec.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.0
Hmm I'm not quite sure :c In your attempt at the problem, where is the 140 degree angle coming from?
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
180  40 = 140.
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
(In the parallelogram)
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Did you have a positive or negative value for cosine?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
What did you get for the magnitude?
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
It would be negative since the 140 is to the left of the y axis
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Sounds good. So your magnitude is greater than 13? What did you get? Is it a matter of number of decimals?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
@thechocoluver445 are you still there?
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
It's supposed to be 9.8 but I keep getting 19. something!
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
I'm pretty sure my way makes sense, but I don't know.
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
I just realized that my way was correct. Since the resultant is opposite an obtuse angle, it must be the longest side of the triangle. Thus, 9.8 cannot be the right answer! So I was correct. Thanks to everyone for helping. :)
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
19.8 is correct for the problem you have posted..
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
The answer key was just wrong, lmao!
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
Yeah, that's what I got lol!
 one year ago

thechocoluver445Best ResponseYou've already chosen the best response.1
She probably just forgot the 1 before the 9.8 haha
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
The only thing you may want to check to see if there are typos. It is possible that they modified the question but forgot to modify the key (which is half of the current answer).
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Oh, so it's not a printed key! That make it even more probably that the answer is wrong.
 one year ago
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